A video is a series of many pictures where the moving parts only move a tiny distance in each frame. When played back at the same speed as they were filmed, they reproduce the movement. When the speed slows down the motion becomes slower.
The many photos in the series can be edited frame by frame with high tech video editing software. To make such a video, you would first make a slow motion video that will be the background and a normal video of the singer in sync with the music and copy only the area of the mouth to the same area of the background frame by frame.
It takes a lot of skill both in the filming and editing to do it successfully. The mouth areas in both films have to be the same size and filmed at the same angle and light.